Download Comprehensive and reliable diagnostics for the corona of laser

University of California, San Diego
UCSD-CER-05-06
Comprehensive and reliable diagnostics for the
corona of laser-produced plasmas
Y. Tao, M. S. Tillack, S. S. Harilal,
B. O’Shay, K. Sequoia, and F. Najmabadi
September, 2005
Center for Energy Research
University of California, San Diego
9500 Gilman Drive
La Jolla, CA 92093-0420
Comprehensive and reliable diagnostics for the corona of
laser-produced plasmas
Y. Tao, M. Tillack, S.S. Harilal, B. O’Shay, K. Sequoia, and F. Najmabadi
Mechanical and Aerospace Engineering Department
and the Center for Energy Research
University of California, San Diego
Abstract: Comprehensive and reliable diagnostics for the corona of laser-produced plasmas,
including optical interferometry, Shack Hartmann wave-front sensor (SHWS), Thomson scattering,
13.5 nm extreme ultraviolet (EUV) shadowgraphy, and x-ray absorption spectroscopy are proposed
to be developed utilizing a small scale, affordable experimental platform, which consists of a 500
mJ/150 ps commercial Nd:YAG laser, a 650 mJ/7 ns Nd:YAG laser and a vacuum chamber with a
diameter of 40 cm. SHWS and 13.5 nm EUV shadowgraphy are completely new technologies, and
SHWS has a great potential to be extended into x-ray wavelengths with low cost. A comprehensive
set of plasma parameters in the corona including electron and ion density profiles, temperature
profile, and ionization charge state distribution etc. with high spatial and temporal resolutions will be
measured. Results from various methods can be compared with each other (for example, electron
density profile can be measured by both interferometry and Hartmann wave-front sensor, ion density
by both 13.5 -nm EUV shadowgraph and x-ray absorption spectroscopy, temperature by both
Thomson scattering and x-ray absorption spectroscopy), such that more reliable data can be expected.
This research will provide comprehensive and reliable experimental plasma parameters in the corona
to benchmark hydrodynamic and atomic codes, which play a key role in designing laser plasma
interaction experiments in the fields of 13.5nm EUV lithography (EUVL) source, soft x-ray source,
and research relevant to laser fusion etc. Technologies, facilities, and experiences of plasma
diagnostics will be developed and accumulated, fostering opportunities to carry out research on
plasma diagnostics in the field of laser fusion, high energy density physics, and magnetic
confinement fusion.
1
1. Background
High power laser produced plasmas (LPPs) are highly transient media with high gradients both in
temperature and density, having various applications in a wide range of fields, like nuclear fusion
energy, biology, life science, material science, and the semiconductor industry
[1][2][3]
etc. Knowledge
of the plasma parameters is fundamental to understanding physical processes in laser plasma
interactions, which have a long history and have been greatly motivated by research on laser fusion
and x-ray lasers
[4][5]
. However, because of the large variety of materials, various application fields
under a wide range of experimental conditions, and the complexity arising from steep gradients in
density and temperature profiles, plasmas diagnostics has been one of the most active areas in
modern physics until now
[6][7][8]
, especially for some high Z materials that are interesting in specific
applications of extreme ultraviolet lithography (EUVL), soft x-ray sources, and laser plasma
interactions related with laser fusion. Because most of the previous diagnostics were carried out
using large-scale laser facilities, especially when comprehensive and reliable parameters with
temporal and spatial resolutions were required, most of the efforts focused on a limited number of
materials in limited fields, like laser fusion, x-ray lasers etc. In fact, a wide range of applications of
LPPs are being investigated in a huge number of small groups distributed widely through universities
and industry. Most of the small group can’t afford expensive, complicated, and large scale laser
facilities. And the small available laser energy limits the achievable plasma size in some applications,
making detailed diagnosis a challenge. So there is a great need to demonstrate comprehensive and
reliable diagnostics utilizing a compact, affordable laser system, so that the diagnostics can be
applied to wide application fields under various experimental conditions.
The corona is the region from well under-dense to critical density in laser-produced plasmas.
Most of the important phenomena of laser plasma interaction, like absorption of laser energy,
ionization, radiation generation and transport, and nonlinear scattering etc., occur in this region. And
most of the radiation in the EUV and soft x-ray wavelength range (1-100 nm) comes from this
region. Therefore, well-characterized corona parameters are necessary for the applications of EUVL
sources, intense soft x-ray sources, and laser fusion.
EUVL will hopefully be next generation lithography tool in the semiconductor industry for
fabricating several 10 nm electronic nodes. However, challenges must be addressed before applying
it to mass-production. One is development of a powerful, efficient, clean, and long lifetime 13.5 nm
EUV light source. Laser produced Sn-based plasma has been one of the most promising sources, it
has shown the highest conversion efficiency until now, 3% in 2% bandwidth
2
[9]
. But the physics of
generation and transport of 13.5 nm EUV light in laser produced Sn-based plasmas has never been
completely understood, because of the huge number of transitions in a high Z material and steep
gradients in density and temperature. There is a great need to validate hydrodynamic and atomic
codes employed to optimize EUVL LPPs with reliable and comprehensive measurements of plasma
parameters. Previous works have shown that efficient 13.5 nm EUV light mainly comes from the
corona in Sn-based plasmas due to less opacity
[6][10]
. Low density Sn-doped foam target has shown
comparable conversion efficiency with solid density Sn with much less debris from Sn, and
additional C and O particles can be mitigated efficiently by ambient gas, magnetic, and electric fields
etc. However most of the efforts in developing EUVL sources focus on characterization of properties
of EUV light
[11][12][13]
, there are very few experimental data of plasma parameters, especially for low
density Sn-based targets.
Soft x-rays in a wide wavelength range generated from laser-produced plasmas have many
applications in microscopy, lithography, and surface modification of materials. Wavelengths located
between the k-edges of carbon (284.2 eV) and oxygen ions (543.1 eV) are called the water window,
having a great potential to be applied to x-ray microscopy in life sciences because of their high
contrast between water and organic tissues. Understanding and optimizing plasma physics are critical
to develop an efficient, clean, and long-life time soft x-ray source for these applications
[2][14]
. For
example, there has been a long history to optimize density profile to achieve high conversion
efficiency, however there are few data to characterize the density profile and correlate it with the
properties of x-rays.
Laser plasma interactions in the corona are also important to laser fusion, because the National
Ignition Facility (NIF) target designs use hohlraums filled with gas
[15]
, in which focused high
intensity laser beams ionize the gas and pass through the corona to reach the radiation-converting
wall. Plasma parameters in the corona, such as density and temperature profiles, play an important
role in the generation of scattering light and the formation of filaments, which influence laser beam
transport and result in asymmetry of irradiation. Recently, there has been an intention to use 2ω light
to achieve ignition, because of higher available laser energy. However, most of the previous work on
laser plasma interactions using the Nova facility focused on ultraviolet light, so investigation on the
interaction of green laser light with coronal plasmas has become a hot topic in laser fusion research
[8][16]
.
Hydrodynamic and atomic codes are standard tools to understand and to optimize the physics
of laser plasma interactions. Hydrodynamic codes include LASNEX
3
[17]
, ILESTA
[18]
, MEDUSA
[19]
,
HYADES
[20]
, and HELIOS
[21]
etc. Atomic codes include COWAN
[22]
, FLY
[23]
, Cretin
[24]
and
SPECT 3D [21] etc. However to date, it is still hard to compare experimental and simulation results for
some specific materials under the specific experimental conditions, such as laser-produced Sn-based
plasmas for EUVL source
related with laser fusion
[26]
[25]
and radiation transport in laser-produced metal doped foam plasma
, the reason is the availability and accuracy of experimental data under the
corresponding experimental conditions.
The purpose of this proposal is to demonstrate comprehensive diagnostics for the corona of
laser-produced plasmas utilizing a compact and affordable experimental platform. We will provide
reliable-experimental data to benchmark hydrodynamic and atomic codes used to understand and to
design laser plasma interactions related with EUVL sources, laser fusion, and soft x-ray sources. We
will describe the lasers and vacuum chamber used in experiments. The principle, feasibility,
advantages, and experimental arrangement of the diagnostics, including optical interferometry, Shack
Hartmann wave front sensor, Thomson scattering, 13.5 nm EUV shadowgraphy, x-ray absorption
spectroscopy, and others, will be discussed in this report.
2. Lasers and vacuum chamber
Because intense laser-produced plasma is highly transient, a short pulse probe beam is
required to avoid time-integration effects. Temporal evolution of plasma arises from two facts:
one is the specified temporal profile of the laser pulse and the other is rapid thermal expansion
arising from high gradients both in density and temperature. As an example, for EUVL source
plasmas, typical pulse widths of laser pulses are 5-10 ns (10-9 s); sub-ns is short enough to
distinguish the phenomena occurred at different times within laser pulse. The thermal expansion
velocity in the corona can be described as, Cs = ZTe / M in which Z , Te and M i are the
average charge state, plasma temperature, and mass of ions. Typical plasma temperatures
favorable for efficient 13.5 nm EUV light are from 30 to 60 eV. The preferred averaged
ionization state is Z = 10 , and C s is about several times 10 6 cm/s. If spatial resolution around
several micrometers is required, then a pulse duration of ~100 ps is required. D.S.Montgomery et
al [27] have shown that a steady plasma state can be achieved within 200 ps for plasma generated
by ns laser.
Using a short pulse, temporal resolution can be achieved by verifying the delay time
between the pump and probe laser pulses. Critical density and refraction effects require short
4
wavelength. Interferometry and SHWS require very small laser energy, but Thomson scattering,
x-ray shadowgraphy and x-ray absorption spectroscopy require relatively large energy.
The EKSPLA SL335/SH [28] will be employed as the probe laser. This picosecond (10-12 s)
Nd:YAG laser consists of a self-seeded Q-switched master oscillator, a stimulated Brillion
scattering (SBS) compressor, and two stages of power amplifiers. It produces 1.064 µm laser
pulses at with pulse energy of 500 mJ, pulse duration varying from 150 to 550 ps. When it is
used as probe laser, the shortest pulse duration is always selected. Second and fourth harmonics
are available, the corresponding energies are 240 and 60 mJ respectively. The line width is less
than 0.1 cm-1 at 1.064 µm. The near field pattern is close to Gaussian as illustrated in Fig. 1. If
the beam divergence is less than 0.5 mrad, then intensity on the target up to 1×1014 W/cm2 can be
expected using a focus lens with focal length of 100 mm. Short pulse and low external triggered
jitter (<0.5 ns) enable high time resolution to perform research utilizing double pulses by
synchronizing with another ns laser.
Plasmas will be generated by the EKSPLA laser or by a ns Nd:YAG laser. The ns laser
provides 1.064 µm pulses with energy of 650 mJ, pulse duration of 7 ns, at 10 Hz. In
experiments, laser intensities on the target can be varied from 1010 to 1014 W/cm2, pulse
durations from 150 ps to 7 ns. Experiments under favorable conditions for EUVL sources, soft xray sources, and laser plasma interactions related to laser fusion will be carried out. The two
lasers are synchronized with jitter less than 0.5 ns. The jitter is also monitored by a fast
photodiode equipped with a 500 MHz digital oscilloscope.
Fig.1 Near field pattern of SL335/SH laser beam
5
A vacuum chamber with 40 cm diameter and vacuum below 10-6 Torr will be employed to
contain the laser plasma interactions. An automated target positioning system suitable for high
repetition rate operation will enable accurate positioning in three dimensions. Two monitor
cameras in two directions, i.e. normal view and side view, will be installed. The resolution of the
target position and monitor system is less than 20 µm.
3. Diagnostic technologies to be developed
3.1 Optical Interferometry
Optical interferometry is a convenient means to deduce electron density profile in the under
dense region
[4]
. The phase variation induced by plasma is recorded in an interferogram, and is
related with the electron density ne by,
2π L
δϕ ( x, y ) =
[n( x, y, z ) − 1]d z
λ ∫0
where n = (1 − ne / nc )1 / 2 is the refractive index of plasma , and
(1)
nc = 1.1 × 10 21 λ−2 is the critical
density with the probe wavelength λ in micrometers. Short probe wavelength allows access to
higher plasma density, and longer wavelength is preferred to obtain a significant phase shift in
the under-dense region.
Relatively large-scale plasma size is required for efficient EUVL sources [9] and laser fusion
research, and there is a steep gradient in density profile. The refraction induced by the electron
density gradients can’t be neglected and limits the application of interferometry in these cases.
Rays associated with the probe beam that initially propagate parallel to the target surface will
bend toward regions of low density. This introduces two effects on the interferogram: one is the
limitation of the accessible maximum density because of finite collection angle of the imaging
optics, and the other is the error on spatial resolution. The angle of refraction may be
approximated as[29],
θ = L(
n e (z )
)
ncls
6
(2)
where L is the length of plasma, z is the distance from the target, and ls is the scale length of
plasma. Assume that the plasma density profile is given as, n e ( z ) = n e 0 exp(− z / l s ) . Then the
error σ induced by the deflection of the rays can be approximated as σ = L • θ . For L ~ 300 µm,
in order to control the total error under 20 µm, the error of refraction should be less than < 15
µm, so that θ<0.05. The maximum accessible electron density ne is ~ 6×1019cm-3 for a 532nm
probe beams by assuming ls ~ 200 µm . As such, F/20 imaging lenses are used.
An experimental arrangement using a polarization interferometer is illustrated in Fig.2. A small
part split from the EKSPLA laser beam is converted into 2ω (532 nm) by a type II KDP crystal and
used as probe beam. A λ/2 wave plate and polarizer are used to adjust the energy and rotate the
polarization of the probe beam. The polarization is set at an angle of 45 degrees with respect to the
optical axis of a Wollaston prism. A convex F/20 lens relays the plasma image to the imager (visible
CCD camera). The Wollaston prism splits the probe beam into two beams with orthogonal
polarization. The second polarizer is used to adjust the intensities of the two beams to achieve equal
intensity and equal polarization in the overlap area. In this arrangement, the part distorted by the
plasma contained in one beam will interfere with the un-distorted part of the other beam. A narrow
band interference filter is employed to shield the detector from plasma emission.
Polarizer F/20 lens
b
Wollaston
prism
D
Interference
filter
CCD
camera
λ/2 WP
Polarizer
Fig.2 Experimental arrangement of polarization interferometer
The fringe distance is determined by, δi =
D
λ , where D is the distance from the prism
b•ε
to the imager, b is the distance from the rear focus of the imaging lens to the prism, and ε is the
split angle of the Wollaston prism. In our arrangement, b can be varied from 200 to 400 mm,
b+D=900 mm, ε=10 mrad, then δi = 75 − 150 µm (in the image plane), and δi = 7.5~15µm (in the
target plane). The magnification is given by, M =
7
f +b+ D
= 10 , where f=100 mm is the focal
f
length of the imaging lens. Recalling the error induced by refraction, the spatial resolution will
be about 20 µm, and will be calibrated in experiments. The temporal resolution will be better
than 200 ps by monitoring the jitter between probe and pump laser pulses. If the size of the CCD
camera is 8×8mm, the field of view on the target is 800 µm. The probe beam size will be 2-3 mm.
The phase shift is extracted by mathematical treatment based on the Fast Fourier Transform
(FFT) method from two interferograms [30]; one is obtained with plasma and the other is obtained
without plasma (the reference). The intensity profile of the interfergram containing the distorted
phase induced by plasma can be described as,
I( z i , x ) = 2I 0 ( z i , x ) + c( z i , x ) exp[ 2πf0 x )] + c * ( z i , x ) exp[ −2πf0 x )]
(3)
with c( z i , x ) = I 0 ( z i , x ) exp[iΔφ( z i , x )], and its conjugate c* contains all the information relative
to the phase shift Δϕ induced by the plasma. f0 is the spatial frequency of fringes. 1 -D FFT with
respect to the x-axis is applied,
F( z i , f ) = F0 ( z i , f ) + C( z i , f − f0 ) + C * ( z i , f + f0 )
(4)
Since the spatial frequencies of I 0 ( z, x ) and φ( z, x ) are much lower than f0 , the Fourier spectra
are separated by f0 . C( z i , f − f0 ) contains all the desired information ; the other two items in
equation (4) are shielded away. Unwanted background signal is removed in this process. The
inverse FFT of C in the plasma case gives, c p ( z i , x ) = I 0 ( z i , x ) exp[iφ( z i , x )] . And the i nverse
FFT of this component in the reference interferogram gives, c r ( z i , x ) = I 0 ( z i , x ) . Then the phase
shift is obtained from the imaginary part of the logarithm of the ratio Im age[log( c p / c r )] .
Laser-produced plasmas are often cylindrically symmetric, so that Abel inversion can be
used to extract a density map from the phase map. The symmetric axis is the x axis (along the
laser incidence line). By using Abel inversion, the equation can be rewritten as
k 0 [n(r, x ) − 1] = −
1 r0 dφ( z, x )
dz
[
]
∫
2
r
π
dz
z − r2
r0 dφ( z, x )
λ
dz
ne (r , x ) = − nc ∫ [
]
r
π
dz
z2 − r 2
(5)
(6)
Interferometer Data Evaluation Algorithm (IDEA) will be used to calculate the Abel
inversion[30], where f-interrogation and FFT methods are adopted. The number of the cubic
polynomial was optimized for each line.
8
Using this method, measurements of electron density profile of laser-produced plasma
related with 13.5 nm EUVL source will be performed. Various targets, such as, bulk solid
density Sn, foil Sn, thin coating Sn, low density Sn-doped foam, and Li targets will be
investigated. The relation between the properties of 13.5 nm EUV light and plasma density
profile will be examined in detail. Effects of plasma density profile on soft x-ray generation will
be checked. The transport of high intensity laser in underdense plasma will be studied, which is
related with indirect-drive ignition of laser fusion.
3.2 Hartmann wave-front sensor
Turbulent
medium
Distorted wave-front
imager
Plane
wave
Fig. 3 Principle of Hartmann wavefront senor
A wave-front is the surface in which all of the points have the same phase. Light waves can
be divided into plane, spherical, and others waves corresponding to their wave front. The central
part of a Shack Hartmann wave-front sensor (SHWS) is a micro lens array. A plane wave
incident on a SHWS is broken into beamlets and produces an array of spots located on the
optical axis (dash line) of an individual lens on the imager, as illustrated in Fig. 3. When the light
passes through a non-uniform medium, such as a turbulent atmosphere, phase distortion will be
added to the wave front of the incident light beam. The distorted wave-front produces a local
gradient in the phase, ∇φ , displacing the spot from the axis, shown as the red line. Each
individual spot is displaced from the axis by a distance s =
∇φ • f • λ
, where λ is the
2π
wavelength of the incident light and f is the distance from the Hartmann lens array to the
detector. The individual spot displacement directly provides the corresponding phase tilt in the
place of the lenslet, so that the distorted wave-front can be reconstructed. Comparison between
9
the incident wavefront and the distorted wavefront can provide the density distribution of the
nonuniform medium.
There is a very steep density gradient in the laser-produced plasma. As light rays propagate
through the plasma, their phase is altered by the gradient of electron density and the wavefront is
distorted. A SHWS measures the local wavefront tilt perpendicular to the probe light, if the
probe light passes through the plasma perpendicular to the plasma expanding direction, A SHWS
can provides the 2-D density gradient distribution in the plane x-y, where x is the expansion
direction and y is parallel to the target surface [31]. The local phase tilt due to a plasma gradient is
given by
∇k =
2π
ω1
∇n = −
λ
c 2
1
1
∇ne
ne ncr
1−
ncr
(7)
The feasibility of SHWS to measure phase distortion induced by a programmable liquid crystal
has been demonstrated [32].
In principle, a SHWS can easily be extended into x-ray wavelengths, because it does not
require coherent light. Under the benefit of efforts of EUVL source development, a bright 13.5
nm EUV light based on a small-scale commercial laser is ready to be used. And multi-layer EUV
mirrors with high reflectivity at normal incidence are commercially available, which can collect,
collimate, and focus 13.5 nm EUV beam with high transport efficiency. Due to small refraction
and high corresponding critical density (6×10-24 cm-3), 13.5 nm EUV light can penetrate the
dense plasma region. It will be a powerful and low cost tool to diagnostic plasma density profile
in dense region compared with x-ray laser interferometer, which requires complicated
experimental arrangement and a large-scale laser facility [33][34]. Dense region of LPPs is greatly
interesting in the fields of laser fusion, high energy density physics etc.
For an EUV SHWS the only difference from the visible version is the ‘micro-lens array’.
For EUV light, reflective mirrors can only be used because of its heavy absorption in any
materials. Fortunately, multi-layer Mo/Si coating are commercially available on various
substrates [35], which has a 70% reflectivity centered at 13.5 nm at normal incidence, so a micro
concave spherical mirrors array coated with multiplayer Mo/Si coating is affordable and will be
used as a ‘micro lens array’. Another choice for EUV ‘micro lens array’ is a Hartmann mask.
10
Until now, there is no experimental measurement on practical plasma using SHWS even
with visible light. So first, it is important to demonstrate its ability to measure real density
profiles of LPPs. The feasibility of this technique applied to practical laser-produced plasmas
will be examined, experiences for system design will be accumulated, and software for data
processing will be developed with a very low cost. If successful, it will be become much easier
to find funding to extend this new technology to x-ray wavelengths. Designation of 13.5 nm
EUV SHWS will be performed.
The experimental arrangement is similar to interferomery: a small part of the laser beam
split from the EKSPLA laser will be converted into 2ω (532 nm) and used as a probe beam. The
probe beam passes through plasma and is relayed to a SHWS. A SHWS facility (CLAS-2D from
Wavefront Science Inc.) in the laser laboratory at UCSD will be employed. An automatic code
will be developed and employed to extract a phase map from SHWS. Abel inversion will be
employed to achieve density map. Measurement of electron density profile using SHWS for
laser-produced plasmas under the favorable conditions for efficient 13.5 nm EUVL source will
be carried out. The results will be compared to the results from optical interferometry under the
same conditions.
3.3 Thomson scattering
Laser-based Thomson scattering (TS) provides a wavelength shift due to electron motion in
the local electric field [36]. It has been adopted as a fundamental diagnostic of plasma parameters
and basic processes in laser produced plasmas [37], because its data processing does not depend
on complicated models compared with other methods, like x-ray spectroscopy
[38]
. Electron
−
temperature, Te, electron density, ne, the averaged ionization stage, Z , ions temperatures, T i, and
relative ion concentration of plasma can be measured with high accuracy [37].
TS is characterized by the scattering parameter α, which is proportional to the ratio of the
probe scale length λs =
given by λD (cm) =
λ probe
λ
sin(θ / 2) to the Debye length, α = s , where Debye length is
2
2πλD
Te
T [ev]
= 743( e − 3 ) . For α < 1 , it is collisional collective TS, for α > 1 ,
2
4πne e
ne [cm ]
it is called collective TS. Our plasmas of interest, with low density and moderate or high
temperatures, fall into the collective scattering regime. The dominant source of scattering comes
11
from correlated long-wavelength density fluctuations rather than random motion of individual
electrons (ions), i.e., scattering is dominated by high-frequency electron plasma waves (EPW or
Langmuir wave) and low-frequency ion acoustic waves (IAW).
The spectrum induced by IAW will be characterized by two shifted peaks, one is red
shifted ( ωia = −kia cs ) and the other is blue shifted ( ωia = kia cs ), where k ia is the scattering vector,
and the frequency separation of the two peaks is twice the ion acoustic frequency ω ia ,
(
ωia 2 Te
Z
T
T
Z
) ≅
(
+ Γi i ) ≈ e (
)
kia
M i 1 + kia λD
Te
M i 1 + kia λD
(8)
where M i is the ion mass, Ti is the ion temperature, Γi is the specific heat ratio, and the length of
the scattering vector kia is given by the triangle relation shown in Fig. 4. For highly ionized
plasma, Ti << Te .
Pump laser
Probe laser
To Detector
kin
kia
ks
Fig.4 Illustration of experimental arrangement for Thomson Scattering.
The propagation direction of the ion acoustic wave in the plasma is determined by the
scattering vector k ia = k scat −k in , where k scat and k in are wave vectors of scattered and incident
light. The incident wave vector can be found from the dispersion relation for an EM wave in
plasmas, ωincident = ω p + kin2 c 2 , where ω p is plasma frequency, c is the velocity of light, and
kin =
ω2 ω
ωin
n
1 − 2p = in 1 − e ,
c
ωin
c
ncr
12
(9)
where ne =
meω p2
4πe 2
is plasma density and ncr =
meωin2
is the critical density. Since the frequency of
4πe 2
the scattered light is shifted only by the comparably small ion acoustic frequency, the wave
number of the scattered light is given by k s ≈ kin , then k ia = 2k in sin(θ / 2) . The temperature and
ionization state can be estimated from the frequency separation. However, accurate information
can only be achieved by fitting the IAW spectrum using the following expression for the
scattered power, Ps , into a solid angle dΩ per frequency range dω ,
→
→
→
dPs
k • k e2
cE02 (r )
= in s
dxS
(
k
,
ω
;
x
)
n
(
x
)
dydz
e
∫
dΩdω
2π me c 2 ∫
8π
(10)
→
where E 0 is the probe electric field and ( S ( k , ω ; x) is the dynamic form factor that accounts for
ion-ion collisions having the following form,
4k ia2 [c s2 /(1 + k ia2 λ2D ) + vi ]γ ia
S (k ,ω) =
(ω 2 − k ia2 v s2 ) 2 + 4ω 2 γ 2
→
(11)
−
where v s = [c s2 /(1 + k ia2 λ2D ) + Γi vi2i ]1 / 2 , c s = Z Te / M , vi = Ti / M .The damping of IAW,
γ ia = 2k ia2 vi2 Reη i / 3vi + (π / 8)1 / 2 c s k ia v s / ve and the specific heat ratio,
are
defined
by
the
frequency-dependent
Γi = 5 / 3 + 4ω Imη i / 3vi
ion
η i = iν i (ω + i1.46ν i ) /[(ω + 1.2iν i )(ω + 1.46iν i ) + 0.23ν i2 ] , where the ion-ion
viscosity,
collisional
−
frequency ν i = 4 π Z 4 e 4 ni Λ i / 3M 1 / 2Ti 3 / 2 . A code to calculate the above formulas will be
developed to fit the IAW spectrum.
Frequency shift induced by heavily damped electron plasma waves is achieved by the BohmGross dispersion relation, ω 2 = ω p2 +
3k in2 Te
. The simultaneous observation of IAW and EPW
me
−
spectra offers a unique way to obtain Te , ne , and Z from TS alone. However, large laser pulse
energy is required to observe EPW spectrum
[37]
. We intend to focus on IAW spectrum in this
research.
13
Feasibility using a small energy probe beam
For 532nm probe light, under the conditions of elctron density ne=2×1019/cm3, temperature
Te=60eV, and ionization state Z=10, the approximate wavelength shift is Δλ ~ 0.08nm .
Requirements on the linewidth of the probe beam and resolution of the spectrometer are less than
0.01nm. EKSAPLA laser’s linewidth is less than 0.0025nm (0.1/cm at 532nm). For this research
effort, we plan to use the ELIAS-II high resolution spectrometer obtained from Cymer Corp. The
ELIAS-II provides a maximum spectral resolving power of
25
fm
(http:/www.ltb-
berlin.de/elias.html).
Because plasma emission generated by 1.064 µm pumping laser at intensities from 1011 to1013
W/cm2 is almost a continuum, harmonics can be neglected. And there is only a very small
wavelength deviation of scattered light from the probe light, so that a narrow bandpass filter
(Δλ=1nm) at 532 nm can be employed to shield plasma emission. And we mainly focus on plasma
generated by laser pulse with small energy, so that plasma emission is much lower than
experimentsin laser fusion
[39][40]
. So scattered signal with high contrast ratio is possible using a
relative low probe energy (< 100 mJ)[41].
In experiments, the laser beam from the EKSPLA laser is converted into green light (532 nm),
and passes through the plasma along a line parallel to the target surface. Spatial resolution will be
achieved by moving the focus of the probe beam along the line of plasma expansion. A mask with a
20 µm pinhole will be employed to define the scattering region. The scattered light is collected by a
F/3 lens and relayed onto the slit of the spectrometer. Recalling the resolution of the target positioner
and monitor, spatial resolution will be better than 30 µm. Temporal resolution depends on the pulse
duaration of the probe beam (150 ps) and jitter (0.5 ns) between pump and probe pulses, so temporal
resolution is 0.5 ns. The temporal resolution can be improved to less than 200 ps by monitoring the
jitter using a fast photodiode.
3.4 13.5 nm EUV shadowgraphy
X-ray shadowgraphy is a general way to obtain ion density profiles of plasma. A probe xray beam (backlighter) with intensity I0 passes through plasma along z parallel to the target
initial surface, 2-D shadowgraph in the plane of x and y, where x is parallel to the target initial
surface and perpendicular to z, y is the direction of plasma expansion. Its intensity is attenuated
by absorption induced by ions in the plasma. The output intensity is described as,
14
I ( x, y )
= exp[αρ ( x, y, z )l ( z )]
I0
(12)
where α , ρ , and l are absorption coefficient, density, and length of the plasma. In the
experiment, input and output intensities are measured. If absorption coefficient and length are
known, the ion density of the plasma can be achieved.
For a given wavelength of backlighter and assuming the absorption cross section does not
depend on the temperature, only mass absorption is necessary to consider. Absorption
coefficients at room temperature are well known and tabulated [42], so the product of length and
density can be deduced. A spatially resolved device-a pinhole camera or concave MLM mirror is
employed to relay the x-ray shadow image of the plasma to an imager, like an x-ray CCD camera. In
this way, 2-D shadowgraphs are achieved. Assuming that laser-produced plasma obeys cylindrical
symmetry, Abel inversion can be used to calculate the re-convolution to obtain ion 2-D spatially
resolved density profile. Using a short pulse x-ray backlighter, temporal resolution can be
achieved by verifying delay times between the backlighter driven laser pulse and the pump laser
pulse.
The EKSPLA laser will be used to generate backlighter x-ray sources. Another ns laser will be
employed to generate plasma, with the two lasers synchronized with jitter less than 0.5 ns. The jitter
is monitored for each shot by a fast photodiode. Because of the limitation of driving laser energy, an
efficient soft x-ray backlighter source is required. Fortunately, very efficient 13.5 nm EUV light has
been demonstrated using a small laser energy and low intensity
[9]
. And again combining
commercially available normal incident reflective mirrors enables a bright monochromatic EUV
backlighter at much lower cost than convention x-ray backlighter
[43]
. The experimental arrangement
of an EUV backlighter using a MLM focusing mirror is illustrated in Fig.5. And it is suitable for lowdensity plasmas with moderate temperatures; such plasmas have applications in EUVL source, soft
x- ray source, and laser fusion. The specifications of x-ray shadowgraphy are, Spatial resolution <20
µm, temporal resolution < 0.2 ns.
Backlighter
plasma
Mo/Si
MLM
15
Objective
plasma
MLM
Imager
Fig.5 Principle illustration of bright EUV backlighter using MLM focus mirror
3.4 Spatially and temporally resolved x-ray absorption spectroscopy
X-ray absorption spectroscopy is a powerful tool for analyzing temperature, ionization state
of ions, and density profiles of plasma. The absorption cross section of plasma can be measured
in combination with atomic calculation
[44,45]
. It is also suitable to analyze the characteristics of
the plume, which contains low charge state ions, and is important in debris characterization in
EUVL sources plasmas and laser ablation.
The experimental arrangement is illustrated in Fig. 6. Semi-continuous x-ray light is
generated by focusing the EKSPLA laser to a backlight target. After transmitting through the
plasma to be investigated, the spectrum of x-ray light is recorded by a spatially resolved grazingincidence spectrometer (GIS) equipped with a back-illuminated x-ray CCD camera. In this way,
the spatially resolved absorption spectrum of the targeted plasma can be achieved. Temporal
resolution is achieved by adopting the short pulse duration of the backligter x-ray driven by ps
EKSPLA laser.
Flat-field
1200g grating
wavelength
Backlighter
150ps
Objective slit
space
Plasma
X-ray
CCD
Toroidal mirror
Grazing incident
spectrometer
Fig.6 Experimental arrangement for spatial and temporal resolved x-ray absorption spectroscopy
16
For GIS, when using a spherical mirror as collecting optics, spatial resolution will be lost
due to grazing incidence. Using toroidal focus mirror, stigmatic grazing incidence spectrometer
can achieve spatial resolution around several 10µm [46].
3.5 Other diagnostics
3.5.1 Monochromatic EUV imaging
A concave spherical Mo/Si multilayer mirror will be employed to relay the plasma image to xray CCD camera or EUV light fluorescence glass (Cr:YAG) equipped with visible CCD camera.
Monochromatic (13.5 nm ± 4%) EUV imaging can be taken with spatial resolution <10 µm and high
light flux. This concave multi-layer mirror also can be used to focus EUV light; several µm spot size
is easy to achieve. A high intensity, monochromatic 13.5nm EUV source is useful to carry out
research on the modification and damage of surfaces induced by 13.5 nm EUV radiation, which have
applications in material and life sciences. For example, a TW/cm2 13.5 nm EUV light sources at 10
Hz can be realized using a commercial laser with 1J/10ns/10Hz.
Monochromatic EUV imaging can be used to characterize the process of radiation transport in
LPPs, which is a basic process in laser plasma interaction
[48][49][50]
. Spatial profile of EUV emission
along plasma density gradient will be investigated for low density Sn-based targets in order to
clarify the effect of dominant emission region in density profile in low-density foam targets.
Mo/Si
MLM
Zr filter
Zr filter
Fig.7. Illustration of monochromatic EUV imaging using concave MLM mirror
17
3.5.2 Movable Faraday cup
A movable Faraday cup will be built to study the properties of ions from laser-produced plasmas.
Energy spectrum, angular distribution, and dynamics of ions in ambient gas will be investigated.
Retarding voltage will be applied to analyze the charge state distribution.
3.5.3 Movable EUV energy monitor
A simplified EUV energy monitor will be developed, which consists of a concave spherical
multi-layer Mo/Si EUV (NTT Corp.) mirror and a EUV filtered photodiode (International Radiation
Inc.). The monitor will be calibrated by E-Mon from Jena Corp. It can be moved around the plasma,
to measure the angular distribution of EUV light. The angular distribution is one of the important
characteristics of EUV light and also must be included when conversion efficiency is calculated from
E-Mon measurement, which is always fixed at a specific angle.
Mo/Si
MLM
EUV
PD
Fig.8 Illustration of movable EUV energy monitor
4. Expected results
Demonstration of novel diagnostics
This will be the first time to apply Shack Hartmann wave front sensor to plasma diagnostics. An
assessment to extend it into EUV wavelength will be examined with low cost. Designation and
development of data processing software for 13.5 nm EUV SHWS will be performed. Bright,
compact, and low cost 13.5 nm EUV shadowgraphy will be demonstrated.
Facilities, technologies, and experiences on plasma diagnostics
Facilities, technologies, and experiences for plasma diagnostic will be developed and
accumulated, which provide strong fundamentals to apply for funding to do further research on laser
plasma interactions and their interactions in ‘big’ fields of plasmas, like laser fusion, high energy
18
density physics, magnetic confinement fusion, and x-ray source microscopy for material and biology
sciences etc.
Reliable and comprehensive parameters
Comprehensive and reliable parameters of laser-produced plasma related with applications of
EUVL source, soft x-ray sources, and laser fusion, including electron and ion density profile,
temperature profile, and ionization charge state will be measured in a wide range of experimental
conditions, which are greatly needed to benchmark hydrodynamic and atomic physics codes.
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